Essentials of College Algebra

Transcription

1 Essentials of College Algebra For these Global Editions, the editorial team at Pearson has collaborated with educators across the world to address a wide range of subjects and requirements, equipping students with the best possible learning tools. This Global Edition preserves the cutting-edge approach and pedagogy of the original, but also features alterations, customization, and adaptation from the North American version. Global edition Global edition Global edition Essentials of College Algebra ELEVENTH edition Margaret L. Lial John Hornsby David I. Schneider Callie J. Daniels ELEVENTH edition Lial Hornsby Schneider Daniels This is a special edition of an established title widely used by colleges and universities throughout the world. Pearson published this exclusive edition for the benefit of students outside the United States and Canada. If you purchased this book within the United States or Canada you should be aware that it has been imported without the approval of the Publisher or Author. Pearson Global Edition LIAL_ _mech.indd 1 12/08/14 7:08 pm

2 Essentials of College Algebra GLOBAL EDITION Margaret L. Lial American River College John Hornsby University of New Orleans David I. Schneider University of Maryland Callie J. Daniels St. Charles Community College Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City São Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

3 Essentials of College Algebra, Global Edition Table of Contents Cover Title Copyright Contents Preface Resources for Success R Review of Basic Concepts R.1 Sets Basic Definitions Operations on Sets R.2 Real Numbers and Their Properties Sets of Numbers and the Number Line Exponents Order of Operations Properties of Real Numbers Order on the Number Line Absolute Value R.3 Polynomials Rules for Exponents Polynomials Addition and Subtraction Multiplication Division R.4 Factoring Polynomials Factoring Out the Greatest Common Factor Factoring by Grouping Factoring Trinomials Factoring Binomials Factoring by Substitution R.5 Rational Expressions Rational Expressions Lowest Terms of a Rational Expression Multiplication and Division Addition and Subtraction Complex Fractions R.6 Rational Exponents Negative Exponents and the Quotient Rule

4 Rational Exponents Complex Fractions Revisited R.7 Radical Expressions Radical Notation Simplified Radicals Operations with Radicals Rationalizing Denominators 1 Equations and Inequalities 1.1 Linear Equations Basic Terminology of Equations Solving Linear Equations Identities, Conditional Equations, and Contradictions Solving for a Specified Variable (Literal Equations) 1.2 Applications and Modeling with Linear Equations Solving Applied Problems Geometry Problems Motion Problems Mixture Problems Modeling with Linear Equations 1.3 Complex Numbers Basic Concepts of Complex Numbers Operations on Complex Numbers 1.4 Quadratic Equations Solving a Quadratic Equation Completing the Square The Quadratic Formula Solving for a Specified Variable The Discriminant Chapter 1 Quiz (Sections ) 1.5 Applications and Modeling with Quadratic Equations Geometry Problems Using the Pythagorean Theorem Height of a Projected Object Modeling with Quadratic Equations 1.6 Other Types of Equations and Applications Rational Equations Work Rate Problems

5 Equations with Radicals Equations with Rational Exponents Equations Quadratic in Form Summary Exercises on Solving Equations 1.7 Inequalities Linear Inequalities Three-Part Inequalities Quadratic Inequalities Rational Inequalities 1.8 Absolute Value Equations and Inequalities Basic Concepts Absolute Value Equations Absolute Value Inequalities Special Cases Absolute Value Models for Distance and Tolerance 2 Graphs and Functions 2.1 Rectangular Coordinates and Graphs Ordered Pairs The Rectangular Coordinate System The Distance Formula The Midpoint Formula Graphing Equations in Two Variables 2.2 Circles Center-Radius Form General Form An Application 2.3 Functions Relations and Functions Domain and Range Determining Whether Relations Are Functions Function Notation Increasing, Decreasing, and Constant Functions 2.4 Linear Functions Graphing Linear Functions Standard Form Ax + By = C Slope Average Rate of Change Linear Models

6 Chapter 2 Quiz (Sections ) 2.5 Equations of Lines and Linear Models Point-Slope Form Slope-Intercept Form Vertical and Horizontal Lines Parallel and Perpendicular Lines Modeling Data Solving Linear Equations in One Variable by Graphing Summary Exercises on Graphs, Circles, Functions, and Equations 2.6 Graphs of Basic Functions Continuity The Identity, Squaring, and Cubing Functions The Square Root and Cube Root Functions The Absolute Value Function Piecewise-Defined Functions The Relation x = y2 2.7 Graphing Techniques Stretching and Shrinking Reflecting Symmetry Even and Odd Functions Translations Chapter 2 Quiz (Sections ) 2.8 Function Operations and Composition Arithmetic Operations on Functions The Difference Quotient Composition of Functions and Domain 3 Polynomial and Rational Functions 3.1 Quadratic Functions and Models Quadratic Functions Graphing Techniques Completing the Square The Vertex Formula Quadratic Models 3.2 Synthetic Division Synthetic Division Evaluating Polynomial Functions Using the Remainder Theorem ing Potential Zeros

7 3.3 Zeros of Polynomial Functions Factor Theorem Rational Zeros Theorem Number of Zeros Conjugate Zeros Theorem Finding Zeros of a Polynomial Function Descartes Rule of Signs 3.4 Polynomial Functions: Graphs, Applications, and Models Graphs of f(x) = ax Graphs of General Polynomial Functions Behavior at Zeros Turning Points and End Behavior Graphing Techniques Intermediate Value and Boundedness Theorems Approximating Real Zeros Polynomial Models Summary Exercises on Polynomial Functions, Zeros, and Graphs 3.5 Rational Functions: Graphs, Applications, and Models The Reciprocal Function f (x ) The Function f (x ) Asymptotes Steps for Graphing Rational Functions Rational Function Models Chapter 3 Quiz (Sections ) Summary Exercises on Solving Equations and Inequalities 3.6 Variation Direct Variation Inverse Variation Combined and Joint Variation 4 Inverse, Exponential, and Logarithmic Functions 4.1 Inverse Functions One-to-One Functions Inverse Functions Equations of Inverses An Application of Inverse Functions to Cryptography 4.2 Exponential Functions Exponents and Properties Exponential Functions

8 Exponential Equations Compound Interest The Number e and Continuous Compounding Exponential Models 4.3 Logarithmic Functions Logarithms Logarithmic Equations Logarithmic Functions Properties of Logarithms Summary Exercises on Inverse, Exponential, and Logarithmic Functions 4.4 Evaluating Logarithms and the Change-of-Base Theorem Common Logarithms Applications and Models with Common Logarithms Natural Logarithms Applications and Models with Natural Logarithms Logarithms with Other Bases Chapter 4 Quiz (Sections ) 4.5 Exponential and Logarithmic Equations Exponential Equations Logarithmic Equations Applications and Models 4.6 Applications and Models of Exponential Growth and Decay The Exponential Growth or Decay Function Growth Function Models Decay Function Models Summary Exercises on Functions: Domains and Defining Equations 5 Systems and Matrices 5.1 Systems of Linear Equations Linear Systems Substitution Method Elimination Method Special Systems Applying Systems of Equations Solving Linear Systems with Three Unknowns (Variables) Using Systems of Equations to Model Data 5.2 Matrix Solution of Linear Systems The Gauss-Jordan Method Special Systems

9 5.3 Determinant Solution of Linear Systems Determinants Cofactors Evaluating n x n Determinants Determinant Theorems Cramers Rule 5.4 Partial Fractions Decomposition of Rational Expressions Distinct Linear Factors Repeated Linear Factors Distinct Linear and Quadratic Factors Repeated Quadratic Factors Chapter 5 Quiz (Sections ) 5.5 Nonlinear Systems of Equations Solving Nonlinear Systems with Real Solutions Solving Nonlinear Systems with Nonreal Complex Solutions Applying Nonlinear Systems Summary Exercises on Systems of Equations 5.6 Systems of Inequalities and Linear Programming Solving Linear Inequalities Solving Systems of Inequalities Linear Programming 5.7 Properties of Matrices Basic Definitions Adding Matrices Special Matrices Subtracting Matrices Multiplying Matrices Applying Matrix Algebra 5.8 Matrix Inverses Identity Matrices Multiplicative Inverses Solving Systems Using Inverse Matrices Glossary A B C

10 D E F G H I L M N O P Q R S T U V W X Y Z Solutions to Selected Exercises Answers to Selected Exercises Index of Applications Index A B C D E F G H I J L M Table of Contents

11 N O P Q R S T U V W X Y Z Photo Credits